The sole surviving manuscript dates to the later 13th century BCE (no earlier than the 19th dynasty in the New Kingdom).
The date for the composition of this document is unknown. The papyrus itself (Papyrus Leiden I 344) is a copy made during the New Kingdom of Egypt. The dating of the original composition of the poem is disputed, but several scholars have suggested a date between the late 6th dynasty and the Second Intermediate Period (ca. 1850 BCE-1600 BCE), and appears to describe how the Hyksos took over Egypt.  The theme of this work had previously been taken either as a lament inspired by the supposed chaos of the First Intermediate Period, or as a plea to Pepi II Neferkare depicting the fall of the Old Kingdom. The admonitions may not be a discussion with a king at all however. Otto was the first to suggest that the discussion was not between Ipuwer and his king, but that this was a discussion between Ipuwer and a deity. Fecht showed through philological interpretation and revision of the relevant passages that this is indeed a discussion with a deity. Modern research suggests that the papyrus dates to the much later 13th dynasty, with part of the papyrus now thought to date to the time of Pharaoh Khety, and the admonitions of Ipuwer actually being addressed to the god Atum, not a mortal king. The admonitions are thought to harken back to the First Intermediate Period and record a decline in international relations and a general impoverishment in Egypt.
MA: Why should we consider this, supposedly later, document as a credible source for "pre-fifth" Egypt?
SC: As the Wiki article states: "... The date for the composition of this document is unknown... the dating of the original composition of the poem is disputed, but several scholars have suggested a date..."
So scholars simply do not know for certain the date for the original composition - it's in dispute. But anyway - we are not saying this document is pre-fifth dynasty - only that it tells us "...what the pyramid concealed was emptied..." And it seems this emptying of the pyramids took place during a period of great upheaval in ancient Egypt as one would imagine rapid and catastrophic climate change would bring.